How do you simplify #\frac{(3ab)^2(4a^3b^4)^3}{(6a^2b)^4}#?

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Answer 1 · 2014-11-02T15:14:47

#{(3ab)^2(4a^3b^4)^3}/{(6a^2b)^4}#

since #4=2^2# and #6=3cdot2#,

#={(3ab)^2(2^2a^3b^4)^3}/{(3cdot2a^2b)^4}#

by distributing the powers,

#={3^2a^2b^2 cdot 2^6a^9b^{12}}/{3^4 2^4a^8b^4}#

by collecting like factors,

#={3^2 2^6a^{11}b^{14}}/{3^4 2^4a^8b^4}#

By cancelling out #3^2#, #2^4#, #a^8#, and #b^4#,

#={2^2a^3b^{10}}/{3}=4/3a^3b^{10}#

I hope that this was helpful.